Linear Identification Problems for Equations with the Dzhrbashyan–Nersesyan Derivative

Linear coefficient inverse problems for equations with the Dzhrbashyan–Nersesyan fractional derivative in Banach spaces are studied in the cases of a bounded and of a sectorial operator at the unknown function. The equation is endowed by the Dzhrbashyan– Nersesyan initial value conditions and the overdetermination condition, the form of which is different for the cases of a constant and variable unknown coefficient in the equation. In the case of a constant unknown coefficient we obtain a criterium for the well-posedness of the inverse problem in terms of the characteristic function of the inverse problem. In the case of a variable unknown coefficient, we establish the unique solvability of the problem. are proved. Some applications of the obtained results are discussed.